1. Field of the Invention
The present invention relates generally to a method of displaying an image and more specifically to a computerized method of displaying on a two-dimensional, raster scan display screen an image lying within a three-dimensional space.
2. Description of the Prior Art
In prior computer graphic display methods, graphic image data of an object or objects lying within a three-dimensional space are previously stored in memory as three-dimensional coordinates information; the information data are read from the memory in sequence; and the read data are image-transformed in accordance with predetermined calculation formulas in order to present a solid graphic image on a display screen. When the above image transformation calculations are executed to display an image on the two-dimensional display screen, three methods have usually been adopted to convey an impression of the three dimensional features of the object, namely perspective transformation processing, shawdow processing and hidden surface processing.
By the perspective transformation processing, the feeling of distance can be displayed by changing the size of an object in proportion to the distance to an observing point on the basis of the fact that the near is perceived as large and the far is perceived as small whenever an object is seen through human eyes.
By the shawdow processing, the ups-and-downs of surfaces of an object are displayed by changing the apparent brightness of the illumination on each surface of a graphic image represented on a display screen on the basis of the fact that the inclinations of the outer surfaces of an object are different from each other relative to a light source positioned at a point within a three-dimensional space so that the human eye sees the object as if the brightness on each surface of an object changes.
By the hidden surface processing, the feeling of distance can be represented by not displaying the graphic image of nonvisible portions. This derives from the fact that when objects are seen from an observing point within a three-dimensional space, one cannot see the rear surfaces of an object or the surfaces of backward positioned objects upon which frontward positioned objects are superposed.
These three processings are the methods under consideration by which objects can be solidly displayed if an empirical law obtained when one sees objects positioned within a three-dimensional space is realized in accordance with physical calculations. For the purpose of realizing the empirical law, some algorithms have been proposed.
These processings are effective to a certain extent even if adopted independently. However, if combined, since it is possible to obtain a further natural feeling of solidness, the following two methods have conventionally been adopted as a method of executing these processings by means of a computer:
In the first conventional method, the spatial positional relationship between an observing point, a light source and an object are previously determined; the results obtained by perspective processing, shadow processing and hidden surface processing are written in memory as a series of data; and the data are read from the memory, where necessary, in order to display a graphic image.
In this first method, although it takes a great deal of time in forming a series of data to be written in the memory, there exists an advantage in that it does not take much time to transform the image information. However, there still exist problems in that it is necessary to previously determine the spatial positional information of the observing point, and it is necessary to form a series of data for each observing point when the number of observing points increases or when the observing point moves. Therefore, there exist the drawbacks that it is impossible to finely change the position of an observing point or it is necessary to provide a great scale of memory capacity large enough to store plural series of data. That is, this method can only be adopted in practical use in displaying an object having a relatively simple external shape.
In the second conventional method, the spatial positional relationship between a light source and an object is set so as to be initialized; the perspective transformation processing, the shadow processing and the hidden surface processing are executed by subroutine. When spatial positional information of an observing point is given, the above three processings for solid representation can be executed in sequence, respectively.
In this second method, although the spatial position of an observing point can be freely determined, since the perspective transformation processing, the shadow processing and the hidden surface processing should be executed for each pixel the amount of data processing becomes huge beyond practical use. For instance, in the case when the system is configured by pixels of 1,000.times.1,000 pieces, 1,000,000 times calculations should be repeated in the perspective transformation processing, the shawdow processing and the hidden surface processing for one observing point. Therefore, there exists a problem in that it takes as much as several hours, for instance, for the processing calculation.